Algebra 1 Unit 3 Overview UNIT 3: Families of Functions TIME: 4 weeks UNIT NARRATIVE: This initial unit starts with a treatment of quantities as preparation for work with modeling. The work then shifts to a general look at functions with an emphasis on representation in graphs, and interpretation of graphs in terms of a context. More emphasis is placed on qualitative analyses than calculation and symbolic manipulation. Linear and non-linear examples are explored. Only linear, simple quadratic, and simple exponential functions will be explored in this unit with an emphasis on distinguishing between linear and exponential growth patterns. Additional work with quadratic functions will occur in later math courses. Features of graphs will emphasize increasing/decreasing behavior and intercepts and interpreting their meaning in the context of a situation. Domain and range will be described verbally and symbolically with students able to identify a reasonable domain based on the context given a function represented in multiple ways. Textbook Correlations: Additional Resources HOLT Algebra 1: Chapter 4 Utah Math I Module 4 Linear and Exponential Functions Utah Math I Module 5 Features of Functions ACADEMIC VOCABULARY: domain, range, function notation, fibonacci sequence, recursive process, intercepts, increasing intervals, decreasing intervals, positive intervals, negative intervals, relative maximum, relative minimum, symmetries, end behavior, periodicity, rate of change, step function, absolute value function, asymptote, exponential function logarithmic function, trigonometric function, period, midline, amplitude, exponential growth, exponential decay, constant function, arithmetic sequence, geometric sequence, invertible function, radian measure, arc, sine cosine, tangent, conditional relative frequency, residuals, correlation, causation, correlation coefficient, sample survey, experiment, observational studies, margin of effort, simulation models, subsets, unions, intersections, complements, independent, conditional probability, 2-way frequency table, addition rule, multiplication rule ESSENTIAL QUESTIONS: 1. How are equations used to describe numbers or relationships and solve problems? 2. How does a graphed solution of equations and inequalities in two variables indicate the set of all its solutions? 3. What do the symbols (parentheses, brackets, braces) represent when evaluating an expression? 4. What is a function, how is it written and interpreted? 5. What essential information is indicated when graphing linear and quadratic functions? 6. What essential information is indicated when graphing square root, cube root and piecewise-defined functions? 7. What essential information is indicated when graphing polynomial functions? 8. How can multiple representations of functions help reveal and explain different properties of the function? 9. What method can be used to develop and define inverse functions? 10. How can I describe the relationship between two quantitative variables represented on a scatterplot? 11. How does a function fitted to data help solve problems? 12. What information is needed to interpret linear models? FUSD Unit Overview 2014-2015 Algebra 1 Unit 3 Algebra 1 Unit 3 Overview CLUSTER HEADING & STANDARDS: Understand the concept of a function and use function notation F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Analyze functions using different representations F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). MATHEMATICAL PRACTICE: All mathematical practice standards are addressed in every unit. Those receiving special attention in this unit are bolded. MP 1 Make sense of problems and persevere when solving them. S.ID.7 MP 2 Reason quantitatively and abstractly. F.IF.1, F.IF.2, F.IF.4, F.IF.5, S.ID.7, A.CED.2, A.CED.3, A.REI.10, F.BF.4, F.LE.2, S.ID.6 MP 3 Construct viable arguments and critique the reasoning of others. S.ID.6 MP 4 Model with mathematics. F.IF.4, F.IF.5, S.ID.7, A.CED.2, A.CED.3, A.REI.10, F.IF.6, F.BF.4, S.ID.6 MP 5 Use appropriate tools strategically. F.IF.4, F.IF.7, S.ID.7, A.CED.2, A.CED.3, F.IF.6, F.BF.4, S.ID.6 MP 6 Attend to precision. F.IF.4, F.IF.5, F.IF.7, S.ID.7, S.ID.6 MP 7 Look for and make use of structure. F.IF.9, F.BF.4, S.ID.6 MP 8 Look for and express regularity in repeating reasoning S.ID.6 Interpret linear models S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Supporting Standards Create equations that describe numbers or relationships A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. FUSD Unit Overview 2014-2015 Algebra 1 Unit 3 Algebra 1 Unit 3 Overview Interpret functions that arise in applications in terms of the context F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Build a function that models a relationship between two quantities F.BF.1 Write a function that describes a relationship between two quantities. Construct and compare linear, quadratic, and exponential models and solve problems F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly Summarize, represent, and interpret data on two categorical and quantitative variables S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Learning Outcomes: By the end of course one level, students should be able to explain the following: Linear – x/y-intercepts and slope as increasing/decreasing at a constant rate and also understand the concept that exponential- y-intercept and increasing at an increasing rate or decreasing at a decreasing rate, Quadratics – x-intercepts/zeroes, y-intercepts, vertex, intervals of increase/decrease, the effects of the coefficient of x2 on the concavity of the graph, symmetry of a parabola. Students should manipulate a quadratic function to identify its different forms (standard, factored, and vertex) so that they can show and explain special properties of the function such as; zeros, extreme values, and symmetry. Students should be able to distinguish when a particular form is more revealing of special properties given the context of the situation. Students should be able to write equations for functions by developing the NOW-NEXT form or use the context in which the problem is given to find the equation. Use addition, subtraction, multiplication, and division to combine functions to create other functions. When used in context, interpret the effect the combination of the functions had on the given situation. Students should also be able to identify the effect transformations have on functions in multiple modalities or ways. Student should be fluent with representations of functions as equations, tables, graphs, and descriptions. They should also understand how each representation of a function is related to the others. For example, the equation of the line is related to its graph, table, and when in context, the problem being solved. End of the Unit Assessment: AC Driven INTERDISCIPLINARY CONNECTIONS: FUSD Unit Overview 2014-2015 LITERACY CONNECTIONS: optional Algebra 1 Unit 3 Algebra 1 Unit 3 Overview REMEDIATION Visual aids Scaffolding of basic functions from Common Core Unit 1 and Unit 2 Real-world situations where students can work problems through linear input/output data tables Revisit 7th/8th grade Common Core Standards Start with equations and move into functions Develop lessons with graph vocabulary based on earlier units. Talk moves FUSD Unit Overview 2014-2015 DIFFERENTIATION ACCELERATION Technology Functions applied in the real world Student presentation of self-made applications Start with equations and move into functions Talk moves ENGLISH LEARNERS ELD Literacy Standards Graphic organizers Highlighting : “cloze” activities SIOP strategies Real-world visuals Group collaboration Number talks SPECIAL EDUCATION Small group instruction One on one peer support Smaller size quantities Number Talks Scaffolding of basic functions from Common Core Unit 1 and Unit 2 Real-world situations where students can work problems through linear input/output data tables Revisit 7th/8th grade Common Core Standards Start with equations and move into functions Develop lessons with graph vocabulary based from earlier units. Algebra 1 Unit 3

© Copyright 2020